langs/Racket/DFA.rkt

115 lines
3.6 KiB
Racket

#lang racket
;; (C) Copyright Collin J. Doering 2014
;;
;; This program is free software: you can redistribute it and/or modify
;; it under the terms of the GNU General Public License as published by
;; the Free Software Foundation, either version 3 of the License, or
;; (at your option) any later version.
;;
;; This program is distributed in the hope that it will be useful,
;; but WITHOUT ANY WARRANTY; without even the implied warranty of
;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
;; GNU General Public License for more details.
;;
;; You should have received a copy of the GNU General Public License
;; along with this program. If not, see <http://www.gnu.org/licenses/>.
;; File: DFA.rkt
;; Author: Collin J. Doering <collin.doering@rekahsoft.ca>
;; Date: Aug 27, 2014
;; Description: an implementation of Determinalistic Finite Autamata
(require (for-syntax syntax/parse))
;; Some structures to represent a DFA
(struct dfaState (trans))
(struct dfaEndState dfaState ())
(struct dfaStartState dfaState ())
(struct dfaStartEndState dfaState ())
(struct dfa (alpha start states))
(define (compute-dfa m xs)
(define/match (run-dfa state ys)
[((or (dfaEndState _)
(dfaStartEndState _)) '()) 'accept]
[(_ '()) 'reject]
[((dfaState f) (cons z zs)) (run-dfa (f z) zs)])
(run-dfa (dfa-start m) xs))
(define-syntax (define-dfa stx)
(define-syntax-class transition
#:description "dfa state transition"
(pattern (in (~optional ->) out:id)))
(define-syntax-class state
#:description "dfa state"
(pattern (name:id (~optional (~seq (~and #:end end?))) trans:transition ...+)
#:with (in ...) #'(trans.in ...)
#:with (out ...) #'(trans.out ...)))
;; (pattern (name:id (~seq (~and #:end end2?)) (~optional (~and #:end end?))))
(syntax-parse stx
[(_ name:id alpha:expr start:state rests:state ...)
#:fail-when (check-duplicate-identifier
(syntax->list
#'(start.name rests.name ...)))
"duplicate state names"
#'(define name
(letrec ([start.name
(dfaStartState
(match-lambda [start.in start.out] ...))]
[rests.name
(dfaState
(match-lambda [rests.in rests.out] ...))] ...)
(dfa 'alpha start.name '(start.name rests.name ...))))]))
;; ----------------------------------------------------------------------------
(define-dfa odd-binary (0 1)
[s0 (0 -> s0)
(1 -> s1)]
[s1 (0 -> s0)
(1 -> s1)]
[s2 #:end
(0 -> s2)
(1 -> s1)]
[s3 #:dead (0 -> s3) (1 -> s3)])
;; Odd binary dfa expansion
(define odd-dfa
(letrec ([s0 (dfaStartState (match-lambda [0 s0]
[1 s1]))]
[s1 (dfaEndState (match-lambda [0 s0]
[1 s1]))])
(dfa '(0 1) s0 '(s0 s1))))
;; Even binary dfa expansion
(define even-dfa
(letrec ([s0 (dfaStartState (match-lambda [0 s0]
[1 s1]))]
[s1 (dfaState (match-lambda [0 s2]
[1 s1]))]
[s2 (dfaEndState (match-lambda [0 s0]
[1 s1]))])
(dfa '(0 1) s0 '(s0 s1 s2))))
;; Odd binary dfa macro
;; (define-dfa odd-dfa (0 1)
;; [s0 (0 -> s0)
;; (1 -> s1)]
;; [s1 end
;; (0 -> s0)
;; (1 -> s1)])
;; ;; Even binary dfa macro
;; (define-dfa even-dfa (0 1)
;; [s0 (0 -> s0)
;; (1 -> s1)]
;; [s1 (0 -> s2)
;; (1 -> s1)]
;; [s2 end
;; (0 -> s0)
;; (1 -> s1)])